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A081611 Number of numbers <= n having no 2 in their ternary representation. 6
1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) + A081610(n) = n+1.

a(n) is also the size of the subset of [1...n] when numbers are added greedily so as to not contain a 3-term arithmetic progression, i.e., according to A003278: a(n) = the largest k such that A003278(k) <= n. (Cf. A003002, the size of the optimal (largest) 3-free subset of [1...n]). - R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

G.f. A(x) satisfies A(x)=(1+x)(1+x+x^2)A(x^3). - Michael Somos, Aug 31 2006

G.f.: (1/(1-x))Product{k>=0} 1+x^(3^k). - Michael Somos, Aug 31 2006

a(n)=a(n-1)+A039966(n). - Michael Somos, Aug 31 2006

PROG

(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=3; A=(1+x)*(1+x+x^2)*subst(A, x, x^3)); polcoeff(A, n))} /* Michael Somos, Aug 31 2006 */

(PARI) first(n)=my(s, t); vector(n, k, t=Set(digits(k, 3)); s+=t[#t]<2) \\ Charles R Greathouse IV, Sep 02 2015

(Haskell)

a081611 n = a081611_list !! n

a081611_list = scanl1 (+) a039966_list

-- Reinhard Zumkeller, Jan 28 2012

CROSSREFS

Cf. A007089, A081603, A081608, A061392.

Number of terms in A003278 that are <=n. - R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009

Sequence in context: A095395 A029134 A029130 * A081228 A270826 A003002

Adjacent sequences:  A081608 A081609 A081610 * A081612 A081613 A081614

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 23 2003

STATUS

approved

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Last modified August 27 12:53 EDT 2016. Contains 275905 sequences.